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We present a Lagrangian decomposition algorithm which uses logarithmic potential reduction to compute an ε-approximate solution of the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. We show that this algorithm runs in O(M (ε −2 +ln M)) iterations, a data independent bound which is optimal up to(More)
Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on an n-vertex, m-arc network in at most nm pivots and O(nZm) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm(More)